Answer:
The calculated value of z = - 0.197 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays
Step-by-step explanation:
We formulate the null and alternative hypotheses as
H0: p1= p2 there is no difference in population proportions of households that decorate their houses with lights for the holidays
against Ha : p1≠ p2 (claim) ( two sided)
The significance level is set at ∝= 0.05
The critical value for two tailed test at alpha=0.05 is ± 1.96
or Z∝= 0.05/2= ± 1.96
The test statistic is
Z = p1-p2/√pq(1/n1 +1/n2)
p1= proportions of households decorating in city 1 = 45/60=0.75
p2= proportions of households decorating in city 2 = 40/50= 0.8
p = the common proportion on the assumption that the two proportion are same.
p = [tex]\frac{n_1p_1 +n_2p_2}{n_1+n_2}[/tex]
Calculating
p =60 (0.75) + 50 (0.8) / 110
p= 45+ 40/110= 85/110 = 0.772
so q = 1-p= 1- 0.772= 0.227
Putting the values in the test statistic and calculating
z= 0.75- 0.8/ √0.772*0.227( 1/60 + 1/50)
z= -0.05/√ 0.175244 ( 110/300)
z= -0.05/0.25348
z= -0.197
The calculated value of z = - 0.197 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays
A bag of 100 hard candies included 30 butterscotch, 40 peppermint, 15 strawberry, 10 orange, and 5 banana. The probability that the first candy pulled out of the bag will be butterscotch or strawberry is .45
a) true
b) false
Answer:
true
Step-by-step explanation:
there is 100 candies. That means we can easily turn the amount of each type of candy into a percent. there was 30 butterscotch which means that is 30 percent. There was 15 strawberry which means that is 15 percent. add that and you get 45. This is a shortcut and i advise you use the way your teacher taught you.
[tex]|\Omega|=100\\|A|=30+15=45\\\\P(A)=\dfrac{45}{100}=0.45[/tex]
So TRUE
Michael's team is trying to determine how they can process shipments more quickly. He has convened a large group to come up with some ideas, but only a few people are driving the conversation. Which rule of good brainstorming is this violating? a) All ideas are recorded O b) Make sure everyone participates O c) No one may criticize another person's idea d) Evaluate ideas after everything is on the table
Make sure everyone participates. Therefore, option B is the correct answer.
This violates rule b) Make sure everyone participates. Michael has convened a large group, however only a few people are driving the conversation. In order to have a successful brainstorming session, everyone must participate and all ideas should be heard. This will ensure that all ideas are taken into account and that the team can come up with the best solutions.
Therefore, option B is the correct answer.
Learn more about the data here:
https://brainly.com/question/13650923.
#SPJ1
i will give brainliest and 5 stars if you help ASAP
Answer:
[tex] Area = 240 m^2 [/tex]
Step-by-step explanation:
The area of the right triangle above = [tex] \frac{1}{2}*base*height [/tex].
Where,
base = 16 m
height = 30 m
Plug in the above values into the area formula:
[tex] Area = \frac{1}{2}*16*30 [/tex]
[tex] Area = 8*30 [/tex]
[tex] Area = 240 m^2 [/tex]
Refer to the attachment for solution.
How many ways can you arrange your 3 statistics books, 2 math books, and 1 computer science book on your bookshelf if (a) the books can be arranged in any order
Answer:
720 different ways.
Step-by-step explanation:
Permutation has to do with arrangement. For example, in order to arrange 'n' objects in any order, this can only be done in n! ways since there is no condition or restriction on how to arrange the objects.
n! = n(n-1)(n-2)... (n-r)!
If there are 3 statistics books, 2 math books, and 1 computer science book on your bookshelf, the total number of books altogether is 3 + 2 + 1 = 6 books.
The number of ways that 6 books can be arranged in any order is 6!.
6! = 6(6-1)(6-2)(6-3)(6-4)(6-5)
6! = 6*5*4*3*2*1
6! = 120*6
6!= 720 different ways.
Hence, the books on your shelf can be arranged in 720 different ways.
in the diagram, POS and UOR are straight lines. OQ is the bisector of angle POR . angle POU and angle UOT are complementary angles.Find the values ofx abd y.
Answer:
x = 34° and y = 62°
Step-by-step explanation:
Complementary angles sum to 90°, therefore 90 = 56 + x which means that x = 34°. The angles formed by an angle bisector are congruent and so are vertical angles; this means that ∠SOR = ∠POU = 56° and ∠POQ = ∠QOR = y. Since POS is a straight line, straight lines have a measure of 180° and because ∠POS = ∠POQ + ∠QOR + ∠SOR, we know that 180 = y + y + 56 → 180 = 2y + 56 → 180 → 2y = 124 → y = 62°.
Determine the present value P that must be invested to have the future value A at simple interest rate r after time t.
A = $8000.00, r = 10.5%, t = 9 months
$
(Round up to the nearest cent as needed.)
Answer:
$7,415.99
Step-by-step explanation:
Hello, please consider the following.
[tex]P\cdot (1+\dfrac{10.5\%\cdot 9}{12})=A = 8000 \\\\P = \dfrac{8000}{(1+\dfrac{31.5}{400})}=\dfrac{8000}{1.07875}\\\\=7415.990730...[/tex]
So it gives $7,415.99
Thank you.
Find the Value of X 1. Solve for X algebraically. 2. Using complete sentences, describe your method for finding X.
The value of x using complete sentences is 40 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees. A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
We are given that;
The measure of angles 75,50 and 85
Now,
In triangle 1
50+75+y=180
y=180-125
y=55
In triangle 2
55+85+x=180
140+x=180
x=40
Therefore, by angle sum properties of triangle answer will be 40 degrees.
Learn more about the triangles;
https://brainly.com/question/2773823
#SPJ3
PLZ HELP THANKS! Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
The answer is
15x - y = - 126Step-by-step explanation:
To find the equation of the line we must first find the slope (m)
[tex]m = \frac{y2 - y1 }{x2 - x1} [/tex]
So the slope of the line using points
(-8,6) (-9,-9) is
[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]
So the equation of the line using point (-8,6) and slope 15 is
y - 6 = 15( x + 8)
y - 6 = 15x + 120
Writing the equation in the form
Ax+By=C
We have
15x - y = -120-6
The final answer is
15x - y = - 126Hope this helps you
If x+y=8 and xy =15 find the value of x³+y³.
Answer:
152Step-by-step explanation:
let x= 5 and y= 3x + y = 85 + 3 = 8xy = 155 × 3 = 15x³ + y³ = ?5³ + 3³ = ?125 + 27 = 152[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 99% confidence if (a) he uses a previous estimate of 22%?
Answer:
Sample size n [tex]\simeq[/tex] 1269.15
Step-by-step explanation:
From the information given ,
At 99% of confidence interval,
the level of significance ∝ = 1 - 0.99
the level of significance ∝ = 0.01
the critical value for 99% of confidence interval is:
[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]
= 0.005
[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]
The value for z from the standard normal tables
= 2.58
The Margin of error E= 3% = 0.03
The formula to determine the sample size n used can be expressed as follows:
[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]
where;
[tex]\mathtt{\hat p }[/tex] = 22% = 0.22
Then:
[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]
[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]
[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]
n = 1269.1536
Sample size n [tex]\simeq[/tex] 1269.15
If there are 80 students in a class and 20 are seniors, what proportion of students are not seniors?
Answer:
3/4
Step-by-step explanation:
First find the number that are not seniors
80 -20 = 60
60 are not seniors
The ratio of not seniors to total
60/80
Divide top and bottom by 20
3/4
Answer:
60 students
Step-by-step explanation:
80 -20 = 60
point k is between j and l. if jk = x^2 - 4x , kl = 3x - 2 and jl = 28 write and solve an equation to find the lengths of jk and kl
Answer:
JK=12
KI=16
Step-by-step explanation:
[tex]K\in\ [JI]\ \Rightarrow\ |JK|+| KI |=|KI|\\\\x^2-4x+3x-2=28\\\\\Longleftrightarrow\ x^2-x-30=0\\\\\\\Longleftrightarrow\ x^2+5x-6x-30=0\\\\\\\Longleftrightarrow\ x(x+5)-6(x+5)=0\\\\\\\Longleftrightarrow\ (x+5)(x-6)=0\\\\x=-5\ (excluded)\ or\x=6\\\\\\\Longleftrightarrow\ \\|JK|=x^2-4x=6^2-4*6=36-24=12\\|KI|=3x-2=3*6-2=18-2=16\\\\Proof: 12+16=28\\[/tex]
if A(-1;10) B(0 ;-1) C (-3;2) ,determine whether AB is perpendicular to AC
Answer:
No, they aren't perpendicular
Step-by-step explanation:
Two lines are perpendicular if the product of their slope is - 1. The slope of line AB=(-1-10)/(0-(-1))=-11 and the slope of the line AC=(2-10)/(-3-(-1))=4. Since the product of their slope isn't - 1. They aren't perpendicular.
The length of the segment between the points $(2a, a-4)$ and $(4, -1)$ is $2\sqrt{10}$ units. What is the product of all possible values for $a$? LOTS OF POINTS AND BRAINLIEST TO CORRECT ANSWER!
Answer:
-3
Step-by-step explanation:
The length of a segment is
sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)
sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)
sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)
Combine like terms
sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)
Square each side
( a-3)^2 + (2a -4) ^2) = 4 *(10)
FOIL the left side
a^2 -6a +9 + 4a^2 -16a +16 = 40
Combine like terms
5a^2 -22a +25 = 40
Subtract 40 from each side
5a^2 -22a -15 =0
Factor
(a - 5) (5 a + 3) = 0
Using the zero product property
a-5 =0 5a +3 = 0
a = 5 5a = -3
a=5 a = -3/5
The product of the terms is
5 * -3/5 = -3
In a frequency distribution of 290 scores, the mean is 99 and the median is 86. One would expect this distribution to be:
Answer:
positively skewed to the right
Step-by-step explanation:
The measure of the central tendency is a profound way to describe the mean, median and mode. The measure of central tendency indicates where the center of distribution tends to be. The measure of central tendency provide a validity and answers whether the scores are high or generally low.
In this measure,The mean is usually pulled to the tail. The skewed is determined by where the tail goes, to the right side , it is positively skewed and to the left side , it is known as negatively skewed distribution.
Given that:
In a frequency of distribution of 290 scores,
the mean = 99
the median = 86
One would expect this distribution to be; positively skewed to the right since the mean value is greater than the median value.
how many bit strings of length 10 contain exactly six 1s?
9514 1404 393
Answer:
210
Step-by-step explanation:
The number of combinations of 10 things taken 6 at a time is ...
10!/(6!(10-6)!) = 210
210 bit strings of length 10 will have 6 1-bits.
Using combination
[tex]\\ \sf\longmapsto {}^{10}C_6[/tex]
We know
[tex]\boxed{\sf {}^nC_r=\dfrac{n!}{r!(n-r)!}}[/tex]
[tex]\\ \sf\longmapsto \dfrac{10!}{6!(10-6)!}[/tex]
[tex]\\ \sf\longmapsto \dfrac{10!}{6!(4!)}[/tex]
[tex]\\ \sf\longmapsto 210[/tex]
prove that tan² theta + cot² theta = sec² theta cosec² theta- 2
Step-by-step explanation:
Tan² theta = sec² theta - 1
Cot² theta = cosec² theta - 1
Tan²+Cot² = sec²-1+cosec²-1
= sec²+cosec²-2
Please find attached herewith the solution of your question.
If you have any doubt, please comment.
Find g(-3)+5 if g(x)=2x-1
Answer:
2
Step-by-step explanation:
g(x) = 2x-1
g(-3)+5
2(-3)-1 +5
-6-1+5
-7+5
-2
Help me please thank you
Step-by-step explanation:
To solve for x, we set up our equation like this:
7x - 7 = 4x + 14
Next, we subtract 4x from the right side to cancel it out and then subtract 4x from the left side.
7x (-4x) - 7 = 4x (-4x) + 14
3x - 7 = 14
Then, we add 7 on both sides (to cancel the -7 out and place it on the right)
3x - 7 (+7) = 14 + 7
3x = 21
Finally, we divide both sides by 3 to isolate our variable, x.
3x ÷ 3 = x
21 ÷ 3 = 7
Our final answer: x = 7
Which of the following best defines the midpoint of a segment? A. The point that splits a line segment into two equal parts. B. Any point on a line segment in between the two endpoints. C. When a line segment is split into equal thirds, a midpoint is any point in the middle third. D. Any point that is closer to one endpoint of the segment than the other.
Answer:
A. The point that splits a line segment into two equal parts.
Step-by-step explanation:
A. The point that splits a line segment into two equal parts.
Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
The statement that best describes the midpoint of a segment is the point that splits a line segment into two equal parts.
Learn more about Midpoint:
https://brainly.com/question/5127660
#SPJ5
I need help on this one please
Hi
Income tax is progressive
So with 50 000 we have :
0.02*3000 + 0.03 ( 5000 -3001) + 0.05 ( 17 000-5001) + 0.0575 ( 50 000 - 17 001) = 60+ 59.97+599.95 + 1897.44 = 2617.36
tax is = 2617.36
Was it evaluated correctly?
Explain your reasoning
help i need to turn it in a hour
Answer:
no
Step-by-step explanation:
2(4+10)+20
2(14)+20
28+20
48
A line runs tangent to a circle at the point (4, 2). The line runs through the origin. Find the slope of the tangent line.
Answer:
Slope of the tangent line (m) = 1 / 2
Step-by-step explanation:
Given:
Point A = (4,2)
Origin point = (0,0)
Find:
Slope of the tangent line (m)
Computation:
Slope of the tangent line (m) = (y2-y1) / (x2-x1)
Slope of the tangent line (m) = (2-0) / (4-0)
Slope of the tangent line (m) = 2 / 4
Slope of the tangent line (m) = 1 / 2
2^x [(x+1)^3 -1] =2^x - (x+1)^3 + 1
Evaluate the expression of both of the whole number X values. One will be negative and the other positive. Identify the negative value as a lower bound and a positive value as a upper bound.
Answer:
Step-by-step explanation:
Given
2^x [(x+1)³ -1] = 2^x - (x+1)³ + 1
Lep p = 2^x, and q = (x+1)³ - 1
Then the original equation becomes
pq = p - q
p - q - pq = 0
p(1 - q) - q = 0
p = q/(1 - q)
2^x = [(x+1)³ - 1]/[-(x+1)³]
2^x = [1 - (x+1)³]/[(x+1)³]
2^x = (x+1)^(-3) - 1
.
b) Lấy được ít nhất một quả cầu trắng
Answer:
I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer.
Solve the problem. A retired couple has $120,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 12% per year. How much should they invest in each to realize exactly $11,600 per year? 1) $90,000 at 12% and $30,000 at 5% O2) $80,000 at 127. and $40,000 at 5% 3) $80,000 at 5% and $40,000 at 12% 4) $70,000 at 5% and $50,000 at 12%
ertificates 6.00% per annum ---x
AA bond 11.00% per annum ---y
x + 1 y= 160000 ------------------------1
6.00% x + 11.00% y= 15600
Multiply by 100
6 x + 11 y= 1560000.00 --------2
Multiply (1) by -6
we get
-6 x -6 y= -960000.00
The double number line shows how many meters a dragonfly can fly in 1 second.
Answer: It's B
Step-by-step explanation:
The table that represents the double number line is (b)
How to determine the table of the number line?On the double number line, we have the following points
x: 0 1
y: 0 25
This means that as x increases by 1, y increases by 25.
So, we have:
x: 0 1 2 3 4
y: 0 25 50 75 100
The above is represented by the second table
Hence, the table that represents the double number line is (b)
Read more about number lines at:
https://brainly.com/question/4727909
#SPJ2
What faction of a day is 5hrs 20 mine
Answer:
16/3 hours 5 1/3
Step-by-step explanation:
Answer: 5 1/3
Step-by-step explanation:
Reflect the shape below across the line x = - 2 . Label the new coordinates.please help me.
Answer:
Step-by-step explanation:
There are 4 roads leading from Bluffton to Hardeeville, 10 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon
Answer: 200 ways
Step-by-step explanation:
From the given information:
Total number of roads leading from Bluffton to Hardeeville = 4
Total number of roads leading from Hardeeville to Savannah = 10
Total number of roads leading from Savannah to Macon = 5
We need to find the total number of ways to get from Bluffton to Macon.
Total number of ways to get from Bluffton to Macon = 4 * 10 * 5
= 200
Therefore, there are 200 required number of ways to get from Bluffton to Macon.